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Communication Dans Un Congrès Année : 2024

Hidden But Essential Recipes for Successful Gaussian Process Metamodeling to Support Uncertainty Quantification in Numerical Simulation

Résumé

The value of using Gaussian Process (GP) regression to emulate costly computational codes for uncertainty management is now widely established. The probabilistic metamodel provided by GP-regression, in the sense that it provides a predictive distribution for each new evaluation point, offers great added value, particularly for safety, reliability or risk assessment studies. However, guaranteeing confidence in the use of this metamodel requires two crucial steps: its training on the available learning data and its validation (often by cross-validation process in our application context). We are particularly interested here in the context of given data, small data (number of model simulations limited to a few hundred) and large numbers of uncertain inputs (from a few dozen to a hundred). In this context, building a successful GP metamodel often calls for a preliminary variable selection. Kernel-based methods (HSIC) and associated independence tests are especially appropriate, for screening but also ranking the inputs. Then, particular care is required when estimating GP hyperparameters: going beyond simple maximum likelihood approaches may be wise. Finally, GP validation must include various criteria to assess the preditivity and reliability of the metamodel's entire predictive law. The presentation will focus on recent advances in these three topics, with the aim of providing guidelines and recipes for successful GP metamodeling in the considered application context.
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Dates et versions

cea-04506392 , version 1 (15-03-2024)

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  • HAL Id : cea-04506392 , version 1

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Amandine Marrel, Bertrand Iooss. Hidden But Essential Recipes for Successful Gaussian Process Metamodeling to Support Uncertainty Quantification in Numerical Simulation. SIAM Conference on Uncertainty Quantification (UQ24), Feb 2024, Trieste, Italy. ⟨cea-04506392⟩
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